(a) The magnitude of the angular momentum about the origin of a particle ofmass m moving with velocity v on a path that is a perpendicular distance dfrom the origin is given by m/v|d. Show that if r is the position of the particlethen the vector J =r × mv represents the angular momentum.(b) Now consider a rigid collection of particles (or a solid body) rotating aboutan axis through the origin, the angular velocity of the collection beingrepresented by w.(i) Show that the velocity of the ith particle isVi = w X riand that the total angular momentum J isJ = Σm₁ [r}w - (r; · w)r;].(ii) Show further that the component of J along the axis of rotation canbe written as Iw, where I, the moment of inertia of the collectionabout the axis or rotation, is given by1 = Σm₁p².Interpret pi geometrically.(iii) Prove that the total kinetic energy of the particles is 1².

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Answered: (a) The magnitude of the angular…

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